The Labour party said on Sunday it was willing to work with Eurosceptic Tories to reduce the size of UK contributions to the bailout of troubled eurozone nations and to cut the timescale of UK liability.

The decision puts the coalition government's parliamentary support for its handling of the crisis under explicit threat for the first time.

The potential alliance may reveal a slow shift towards a more Eurosceptic thinking since Labour went into opposition a year ago. The shift is, in part, political opportunism, but also represents a long-standing belief inside the party that the European commission's reaction to the euro crisis has been too deflationary.

Labour is weighing up an alliance with increasingly fractious Tory Eurosceptics over two specific issues likely to return to the Commons in the next few months – a move that could threaten the government's Commons majority on some key votes or, at the very least, politically embarrass the chancellor, George Osborne.

The first is the degree to which the commission is disproportionately drawing on the European Financial Stability Mechanism (EFSM), to which Britain makes contributions, rather than two other bailout funds for which Britain is less liable.

The second could build on anger at the failure of the coalition government to do more to demand the swift introduction of a permanent bailout mechanism from which Britain would be excluded.

The permanent fund, termed the European stability mechanism, is not due to come into force until 2013, and Labour claims the coalition government has not been pressing for an earlier timetable. Details of how it will operate remain sketchy.

The new permanent mechanism, even though it will exclude non-euro members, will nevertheless have to be approved by the Commons as it represents a change to the Lisbon treaty.

It is known that Ed Balls, the shadow chancellor, is increasingly concerned by the state of the eurozone.

Chris Leslie, the shadow Treasury spokesman responsible for Europe, told the Guardian: "We will be quite prepared to work with parliamentarians from any party to make sure the funds to protect eurozone members is not drawn disproportionately from funds to which Britain contributes. We have already provided more than our fair share.

"We will also work with anyone to make sure the government acts more quickly to introduce a permanent mechansim that draws on only eurozone members.

He claimed the EFSM had shouldered a third of the bailout costs, even though it was due to provide only 12%.

Government whips came under sustained assault last week from their own side for using a series of manoeuvres to prevent the Commons voting to instruct the coalition to vote against any further use of the EFSM until a permanent scheme was established from which non-eurozone members were excluded.

There was a rebellion by 30 Tories who claimed £12.5bn of taxpayers' money was set aside to help Greece, Portugal and Ireland.

Labour did not join the rebellion on the grounds that the resolution pushed by Tory Eurosceptics claimed the EFSM was illegal. It was set up by European finance ministers with the agreement of the former Labour chancellor Alistair Darling at the time of the 2010 general election, and Labour does not accept it was illegal.